Question

# 1.You are 18 today want to retire at age 65.   Starting with the day of your...

1.You are 18 today want to retire at age 65.   Starting with the day of your retirement, you would like to have an annuity initially in the amount of \$35,000 per year (but growing at a 3% annual rate) for 35 years.      You will inherit \$30,000 from your long lost uncle when you turn 34 and save that money as part of your financial plan. Assume an interest rate of 7% for all periods? How much must you put into your investment account today to achieve your goal?

2You invest \$12,500 in an investment that will pay you \$25,000 at a future point in time. What is the return on investment for each of the following periods of time?

a. 4 years

b. 7 years

c. 10 years

3You want to retire at age 50; you are 20 years old today.   You want to retire with a \$10,000 perpetuity because you expect to live forever. In order to completely fund that perpetuity, how much do you need to save today in the bank assuming a 10% interest rate.

1) PV of growing annuity = P / (r - g) x [1 - ((1 + g) / (1 + r))^n]

= 35,000 / (7% - 3%) x [1 - (1.03/1.07)^35]

= \$644,389.70

Its value today = FV / (1 + r)^n = 644,389.70 / (1 + 7%)^47 = \$26,798.53

Value of inheritance today = 30,000 / 1.07^16 = \$10,162.04

Investment required today = 26,798.53 - 10,162.04 = \$16,636.50

2) Rate of return, r = (FV / PV)^(1/n) - 1

r1 = (25,000 / 12,500)^(1/4) - 1 = 18.92%

r2 = 2^(1/7) - 1 = 10.41%

r3 = 2^(1/10) - 1 = 7.18%

3) Value of perpetuity at age 50 = 10,000 / 10% = \$100,000

Its value today = 100,000 / 1.1^30 = \$5,731

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